dx

x =

mittlere Änderungsrate:
Steigung der Sekante:

lokale Änderungsrate:
Steigung im Punkt:
Ableitung a. d. Stelle x:

f'

x

h \rightarrow 0

\downarrow

\downarrow

 f'(x) = \lim\limits_{h \rightarrow 0}{\frac{f(x+h-f(x)}{h}}=

f'(x)

b = 1.4 (slider from 0 to 4, step 0.1)
f(x) = b^(x)
x0: 0.37362
P: (x0, f(x0))
dx = 1 (slider from -5 to 5, step 0.1)
xmin = -2 (slider from -5 to 5, step 0.1)
xmax = 2 (slider from -5 to 10, step 0.1)
a = 1
P0: (a, f(a))
pos = If(a < 0, ((xmax - xmin) / 15, 0), Vector[(-((xmin - xmax) / 100, 0))])
ma = 1 (slider from -5 to 5, step 0.1)
Eingabefeld4 = Textfield(dx)
Eingabefeld5 = Textfield(x0)
f1(x) = f'(x)
t(x) = f(x0) + (f'(x0) * (x - x0))
c = Circle(P, 0.2)
A, B = Intersect(t, c)
i = Segment(A, B)
k = 1 (slider from -5 to 5, step 0.1)
X0: (x0, 0)
m: f'(x0)
Text4: "f'(x) =" + m + ""
Q: (x0, f1(x0))
b0: f(1)
Text5: "m(x, x+h)=\frac{f(x+h)-f(x)}{h} = \dots = " + (LaTeX[f]) + "\frac{" + (LaTeX[b0]) + "^{h}-1}{h}"
m0: f1(0)
Text9: "" + (LaTeX[f]) + " \cdot \underbrace{" + (LaTeX[m0]) + "}_{f'(0)}"
d = false
Text1: "f(x) = " + (LaTeX[b]) + "^{x}"